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Byju's Answer
Standard XII
Mathematics
Nature of Roots
48. If (a,0) ...
Question
48. If (a,0) is a point on a diameter of the circle x²+y²=4 then x²-4x-a²=0 must have : A. Exactly one real root in [-9/10,1/10] B. Exactly one real root in [4,49/10] C. Exactly one real root in [0,2] D. Two distinct real roots in [-1,5]
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Similar questions
Q.
If
(
a
,
0
)
is an endpoint of a diameter of the circle
x
2
+
y
2
=
4
, then
x
2
−
4
x
−
a
2
=
0
has
Q.
The polynomial equation
x
3
–
3
a
x
2
+
(
27
a
2
+
9
)
x
+
2016
=
0
has
Q.
If a
ϵ
R- and a
≠
- 2 then the equaiton
x
2
+
a
|
x
|
+
1
=
0
:
Q.
The equation
e
x
−
x
−
1
=
0
has
Q.
Assertion :If equation
a
x
2
+
b
x
+
c
=
0
and
x
2
−
3
x
+
4
=
0
have exactly one root common, then at least one of
a
,
b
,
c
is imaginary. Reason: If
a
,
b
,
c
are not all real, then equation
a
x
2
+
b
x
+
c
=
0
can have one real root and one one root imaginary.
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